Corporate Finance

102
Corporate Finance

where
βL = levered beta (beta at the current level of debt), and
βU = unlevered beta (beta when there is no debt in the capital structure).

We know that:

V = D + E

That is, the value of the firm equals the sum of values of debt and equity.
Multiplying both sides by their respective beta,

βA V = βD D + βE E

Dividing both sides by V

βA = βD D/V + βE E/V

That is, asset beta is the weighted average of debt and equity beta.
If the beta of debt is assumed to be zero (a somewhat restrictive assumption),^5

βA = βE E/V

or βE= βA (V/E)

The beta that we estimate by regressing stock returns against market returns should not be directly plugged
into CAPM. It should be relevered using the above relationship at the target debt ratio and then plugged.
Assume that a company currently has a D/V ratio of 0.3. So E/V is 0.7. The target D/V is 0.5. Let the current
equity beta be 0.50:

βA= βE E/V

Asset beta = (0.50)(0.7) = 0.35

βE at the target debt ratio = βA(V/E)

= (0.35)(1/0.7)

= 0.5

As you can see, the estimate is more than the current beta, for obvious reasons.
Roger Ibbotson Associates, run by Prof. Roger Ibbotson of Yale University, is an authentic source of beta
and cost of capital for US firms. Ibbotson Associates’ Beta Book uses the following methodologies for
estimating betas from historical return data, estimating industry betas, and combining regression betas and
peer group betas to form adjusted betas. A company from the Compustat database is included in his publication
if it meets three conditions. First, a company must have at least 36 months of return data. (Any company
with less than 60 months of return data is marked with an asterisk.) Second, it must have sales greater than
$100,000 in the most recent year. Third, a company must have a market capitalization greater than $10,000
for the most recent month. They use the S&P 500 as market portfolio in the beta calculations.

(^5) The beta of debt is assumed to be zero because debt is priced on the basis of unsystematic, firm-specific, default risk.